The present invention was made with Government support under a grant from the National Science Foundation, and the United States Government has certain rights therein.
This invention relates generally to analysis and characterization of electromagnetic radiation, and more particularly, to analysis and characterization of ultrashort light or laser pulses, the time evolution of which is measured in amplitude and phase with femtosecond resolution by a linear detection technique having single shot capability, i.e., the capability to analyze and characterize a single pulse with one "look".
Several light pulse diagnostics methods have been developed in the last decade. The most common diagnostics method is the second order autocorrelation, which does not provide information on the pulse shape or on its phase modulation. One method of complete pulse characterization that has been successfully implemented makes iterative fittings of the pulse spectrum, the intensity autocorrelation and the interferometric autocorrelation [J.-C. Diels, J. J. Fontaine, I. C. McMichael, and F. Simoni. Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy. Applied Optics, 24:1270-1282, 1985]. This method has permitted direct verification of the pulse shape and chirp predicted by theoretical models of the femtosecond laser and has also proved to have a high degree of accuracy, as can be seen from the sensitivity of the fitting function to the pulse parameters. However, since this parametric fitting procedure implies a previous estimate of the functional dependence of the pulse, the method is difficult to implement for complex shapes and modulations. Naganuma et al. [K. Naganuma, K. Mogi, and H. Yamada. Time direction determination of asymmetric ultrashort pulses from second-harmonic generation autocorrelation signals. Appl. Phys. Lett., 54:1201-1202, 1989; K. Naganuma, K. Mogi, and H. Yamada. General method for ultrashort light pulse chirp measurement. IEEE J. of Quantum Electronics, QE-25:1225-1233, 1989.] using the same set of three data, have developed a systematic and converging fitting procedure. This iterative fitting typically uses 20 to 30 iterations. The convergence of the method has been tested on simple pulse shapes and modulations. It still remains to be determined how well the iteration converges in the case of arbitrary phase and amplitude modulation. A new pulse and chirp measurement method that can completely reconstruct the signal in amplitude and phase from a in a single measurement was demonstrated by Diels et al. [J.-C. Diels, J. J. Fontaine, N. Jamasbi, Ming Lai, and J.Mackey. The femtonitpicker. Conf. on Lasers and Electro-optics, Baltimore, June 1987, 1987; J.-C. Diels. Autocorrelators measure single laser pulses. Laser Focus World, 25:95-100, 1989].
An improved and simplified reconstruction method on data acquired with the same instrument was recently published [Chi Yah and J.-C. Diels. Amplitude and phase recording of ultrashort pulses. J. of the Opt. Soc. Am. B, 8:1259-1263, 1991]. Tests with simulated data show an excellent fidelity in reconstruction after a single iteration.
All these prior methods have in common the use of a nonlinear process where two photon fluorescence or ionization or second harmonic generation is required at the detection point. In contrast, the pulse measurement technique of the present invention is purely linear, and is therefore particularly well adapted to the detection of weak probe signals.
In order to gain further understanding of the problems associated with pulse analysis and characterization, it should be understood that standard second order autocorrelation techniques provide a mere estimate of the temporal scale in which pulse energy is contained. Most experiments involving femtosecond pulses require a much more precise and complete measurement of tile electromagnetic signal. Some examples are given below, to illustrate the importance of a diagnostic technique providing a complete temporal scale for pulse energy.
Because of normal light dispersion in optical components, significant pulse broadening will occur in any instrument involving ultrashort pulses. The pulse duration and shape will not be the same at one location where is it measured, and another location where it is used. However, knowledge of the pulse shape and phase modulation at one point can enable prediction of tile pulse characteristics at a different point where it is needed. In general, a certain amount of downchirp will be desired in order to obtain the shortest pulse after propagation through the normally dispersive optics of the equipment using the short pulses. The pulse shape and chirp (frequency change with time) can be controlled internally [J.-C. Diels, J. J. Fontaine, I. C. McMichael, and F. Simoni. Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy. Applied Optics, 24:1270-1282, 1985] or externally (for instance with nonlinear propagation in fibers or Kerr media or reflection on nonlinear interfaces) to the source. That control is useless unless a complete diagnostic method is available to measure and to enable convergence to the shape and chirp required at the measuring point, so that the desired shape and chirp can be provided at the main interaction point of the experiment.
The above principle applies also to the propagation of ultrashort pulses through the atmosphere. The air is a dielectric with normal dispersion. There is an optimum chirp that will produce the shorter pulse after a given propagation distance. The same general principle applies to the case of nonlinear waveguides such as fibers, in which self-reproducing pulse shapes propagate without distortion for very long distances. In the case of fibers with negative dispersion, these steady state pulses are stable solutions, and are generally at near IR wavelengths. Whether there are stable or unstable solutions, the study of steady state pulse propagation in fibers is another area of research in which accurate amplitude and phase determination of ultrashort pulses is essential.
An important example of application of ultrashort pulse generation is impulsive stimulated Raman scattering [J.Nelson. Stimulated raman scattering. Journal of the Am. Optical Society B, 8:1264-1266, 1991]. Instead of a simple impulse, the signal applied to the sample is modulated at a frequency matching a molecular vibration. More generally, in any type of coherent interaction, the excitation of the medium follows a path that is dependent of the exact shape (in amplitude and phase) of the resonant signal applied to the system. Here again, a diagnostic method is needed to monitor the exact signal driving the resonance.
A typical method to measure transient transmission is the pump-probe technique. Obviously, the resolution is limited by the duration of the pump probe, since it is necessary to wait until the excitation is complete before probing its result. The purpose of this experiment is to determine the complete temporal response (or transfer function) of the material to an signal at the source wavelength. If a complete measurement can be made of the input signal E(t)=[E(t)+c.c.] and of the transmitted signal E.sub.t (t)=[E.sub.t (t)+c.c.], then the transfer function of the material (in transmission) is uniquely defined. The temporal resolution in this technique is as good as the accuracy with which the pulse shape is determined.
It is generally not the total duration of the pulse that determines the temporal resolution in a pump-probe experiment, but either the rise or fall of the pump and probe. If a reasonably good model exists for the process under investigation, deconvolution procedures can be used to extract time constants with an accuracy better than the pulse duration.